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Question Number 134768 Answers: 0 Comments: 5

Question Number 134767 Answers: 0 Comments: 0

Question Number 134764 Answers: 1 Comments: 0

Z = ∫_0 ^( 2) (dx/( (√(∣x−1∣)))) ?

$$\:\mathbb{Z}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\frac{\mathrm{dx}}{\:\sqrt{\mid\mathrm{x}−\mathrm{1}\mid}}\:? \\ $$

Question Number 134763 Answers: 1 Comments: 0

Given a= (3)^(1/3) + (1/( (√3))) Find the value of 3a^3 −9a+1.

$$\mathrm{Given}\:{a}=\:\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3}{a}^{\mathrm{3}} −\mathrm{9}{a}+\mathrm{1}. \\ $$

Question Number 134760 Answers: 1 Comments: 0

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Question Number 134831 Answers: 0 Comments: 0

proof that if R is a commetative ring with unity then an ideal M and R is maximal iff (R/M) is a field.

$${proof}\:{that}\:{if}\:\mathrm{R}\:\mathrm{is}\:\mathrm{a}\:\mathrm{commetative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{unity}\:\mathrm{then}\:\mathrm{an}\:\mathrm{ideal}\: \\ $$$$\mathrm{M}\:\mathrm{and}\:\mathrm{R}\:\mathrm{is}\:\mathrm{maximal}\:\mathrm{iff}\:\frac{\mathrm{R}}{\mathrm{M}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{field}. \\ $$

Question Number 134828 Answers: 0 Comments: 0

∫^( (π/2)) _0 ((sin (((2x)/3)))/(tan (x))) dx =?

$$\underset{\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:\left(\frac{\mathrm{2}{x}}{\mathrm{3}}\right)}{\mathrm{tan}\:\left({x}\right)}\:{dx}\:=?\: \\ $$

Question Number 134753 Answers: 0 Comments: 0

f is defined in [0; +∞[. { ( ),(),((f(0)=ln2)) :}f(x)=∫_x ^(2x) (e^(−t) /t)dt for x>0 1) Given 0≤f(x≤((e^(−x) −e^(−2x) )/x). Calcule the lim f(x) at 0 and +∞. 2) Calculate f ′(x) , give its variation and plot its curve.

$${f}\:{is}\:{defined}\:{in}\:\left[\mathrm{0};\:+\infty\left[.\right.\right. \\ $$$$\begin{cases}{\:}\\{}\\{{f}\left(\mathrm{0}\right)={ln}\mathrm{2}}\end{cases}{f}\left({x}\right)=\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{e}^{−{t}} }{{t}}{dt}\:\:{for}\:{x}>\mathrm{0} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:{Given}\:\mathrm{0}\leqslant{f}\left({x}\leqslant\frac{{e}^{−{x}} −{e}^{−\mathrm{2}{x}} }{{x}}.\right. \\ $$$${Calcule}\:{the}\:{lim}\:{f}\left({x}\right)\:{at}\:\mathrm{0}\:{and}\:+\infty. \\ $$$$\left.\mathrm{2}\right)\:{Calculate}\:{f}\:'\left({x}\right)\:,\:{give}\:{its}\:{variation} \\ $$$${and}\:{plot}\:{its}\:{curve}. \\ $$$$ \\ $$$$ \\ $$

Question Number 134752 Answers: 0 Comments: 0

In a locality, 20% of population have a chronic disease. Among these people who has a chronic disease, 2.5 % have COVID−19. Among the people who don′t have a chronic disease, 99% have not COVID−19. Calculate the probability that one person of this locality has COVID−19 and a chronic disease.^

$${In}\:{a}\:{locality},\:\mathrm{20\%}\:{of}\:{population}\:{have} \\ $$$${a}\:{chronic}\:{disease}.\:{Among}\:{these}\: \\ $$$${people}\:{who}\:{has}\:{a}\:{chronic}\:{disease},\:\mathrm{2}.\mathrm{5}\:\% \\ $$$${have}\:{COVID}−\mathrm{19}.\:{Among}\:{the}\:{people} \\ $$$${who}\:{don}'{t}\:{have}\:{a}\:{chronic}\:{disease},\:\mathrm{99\%} \\ $$$${have}\:{not}\:{COVID}−\mathrm{19}. \\ $$$$\boldsymbol{{C}}{alculate}\:{the}\:{probability}\:{that}\:{one}\:{person} \\ $$$${of}\:{this}\:{locality}\:{has}\:{COVID}−\mathrm{19}\:{and}\:{a} \\ $$$${chronic}\:{disease}.^{} \\ $$

Question Number 134751 Answers: 1 Comments: 0

In my house, there is 250 laptops: 40 are new, 100 are recent and the others are old. A statistic showed that 4% of new laptops are faulty, 12% of recent ones are faulty and 25% of old ones are faulty. Calculate the probability that 1 laptop be new , knowing that it is faulty.

$$\:{In}\:{my}\:{house},\:{there}\:{is}\:\mathrm{250}\:{laptops}:\: \\ $$$$\mathrm{40}\:{are}\:{new},\:\mathrm{100}\:{are}\:{recent}\:{and}\:{the}\: \\ $$$${others}\:{are}\:{old}.\:{A}\:{statistic}\:{showed}\:{that} \\ $$$$\mathrm{4\%}\:{of}\:{new}\:{laptops}\:{are}\:{faulty},\:\mathrm{12\%}\:{of} \\ $$$${recent}\:{ones}\:{are}\:{faulty}\:{and}\:\mathrm{25\%}\:{of}\:{old} \\ $$$${ones}\:{are}\:{faulty}. \\ $$$${Calculate}\:{the}\:{probability}\:{that}\:\mathrm{1}\:{laptop}\:{be} \\ $$$${new}\:,\:{knowing}\:{that}\:{it}\:{is}\:{faulty}. \\ $$

Question Number 134750 Answers: 0 Comments: 0

.....advanced calculus.... prove that:: 𝛗=Σ(1/(n^3 sin((√2) πn))) =((−13(√2) π^3 )/(720)) ...m.n...

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....{advanced}\:\:\:{calculus}.... \\ $$$$\:\:\:{prove}\:\:\:{that}::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\Sigma\frac{\mathrm{1}}{{n}^{\mathrm{3}} {sin}\left(\sqrt{\mathrm{2}}\:\pi{n}\right)}\:=\frac{−\mathrm{13}\sqrt{\mathrm{2}}\:\pi^{\mathrm{3}} \:}{\mathrm{720}} \\ $$$$\:\:\:\:\:...{m}.{n}... \\ $$

Question Number 134746 Answers: 2 Comments: 0

How to calculate lim_(x→−3) ((x+3)/( (√(∣x^2 +x−6∣)))) ?

$${How}\:{to}\:{calculate} \\ $$$${li}\underset{{x}\rightarrow−\mathrm{3}} {{m}}\frac{{x}+\mathrm{3}}{\:\sqrt{\mid{x}^{\mathrm{2}} +{x}−\mathrm{6}\mid}}\:\:\:\:? \\ $$

Question Number 134741 Answers: 1 Comments: 0

lim_(→−3) ((x+3)/( (√(∣x^2 +x−6∣)))) ?

$$\underset{\rightarrow−\mathrm{3}} {{lim}}\frac{{x}+\mathrm{3}}{\:\sqrt{\mid{x}^{\mathrm{2}} +{x}−\mathrm{6}\mid}}\:\:? \\ $$

Question Number 134738 Answers: 0 Comments: 0